Electrical logarithm computer



Feb. 1950 N. D. COGGESHALL 2,497,208

ELECTRICAL LOGARI'I'HM COMPUTER Filed Aug. 27, 1948 2 Sheets-Sheet l I II INVENTOR. 7 5. ORM DicoscagssaagLL Feb. 14, 1950 N. COGGESHALL2,497,208

ELECTRICAL LOGARITHM COMPUTER Filed Aug. 27, 1948 2 Sheets-Sheet 2JNVENTOR. 7170.3 NORMflN D. coseas aa gd 7 fil h;

ATTORNEY Patented Feb. 14, 1950 ELECTRICAL LOGARITHM COMPUTER Norman D.Coggeshall, Verona, Pa., assignor to Gulf Research & DevelopmentCompany, Pittsburgh, Pa., a corporation of Delaware Application August27 1948, Serial No. 46,399

4 Claims.

This invention concerns an electrical appa ratus for computing thelogarithm of numbers and more particularly concerns a logarithmicpotentiometer having a high degree of precision.

In many mathematical computations it is often necessary to determinelogarithms to some pre determined or preassigned base. Such computationsoccur in various general computing systems and are also oftenencountered in various types f control and recording apparatus. Whilevarious empirical means have been devised for electrically obtaining alogarithmic signal, these devices have generally been subject to errorsof calibration and errors in their empirical design which are eliminatedby the present invention. The present invention is useful as an elementof an electric computing machine, and is particularly useful in that thelogarithmic function is inherent in a very simple geometrical design ofthe electric current-conducting medium.

It is accordingly an object of this invention to provide means forgenerating an electrical signal proportional to the logarithm of anumber to which the machine is set.

It is a further object of this invention to provide apparatus forobtaining a logarithm signal of high precision.

It is a still further object of this invention to provide apotentiometer by means of which a logarithmic variation of potential maybe ob tained with a high degree of precision.

It is a still further object of this invention to provide a logarithmcomputer by means of which logarithms may be computed to any desiredbase.

It is a further object of this invention to provide a. logarithmcomputing apparatus which is extremely simple in its construction andwhich is inherently precise.

These and other objects of this invention are attained as described inthe following specification, of which the accompanying figures form apart, and in which Figure 1 is a mathematical diagram used forexplaining the principles of my invention;

Figures 2. and 3 show respectively a top and side view (partly insection) of an embodiment of my invention wherein a circular concentricannular disc is used as the electrical currentcarrying or resistancemedium; and

Figures 4 and 5 show respectively a top and side view of a preferredembodiment of my invention wherein a sector of a circular annular discis used as the current-carrying medium.

' This invention makes use of the fact that when an electric currentflows radially outward in a 2 thin disc there results a radialdistribution of potential which is logarithmic. This may be explained byreference to Figure l, in which numeral.

I indicates a circular disc of uniform resistivity p and uniformthickness t. Assume that an electric current is introduced at the centerpoint 2 and collected uniformly around the periphery of I by an outerring 4 having a low resistance. Since the resistance of the disc alongany radius from 2 to 4 is the same, there will be a uniformcircumferential distribution of the current as it flows radiallyoutward. Let an annular ring of the disc, such as 3, have a radius r anda radial width dr. Then the resistance across this ring will beexpressed by The total resistance of the disc from any inner radius 11out to the radius r may be obtained by' integrating as follows:

R 2h 1; r 2t1[ T111 R= (log r-log r If the current which flows from 2 to4 is i then the potential drop iR will be given by If we let ip/2t1r=,kand make r1=1 then we have simply e=lc log 1.

In this invention such a disc may be of suit concentric annular disc 10,may be of metal foil,

or graphite, or any well known resistance ma'-' terial molded in theform of a disc of uniform thickness and resistivity; or such a disc maycomprise a coating of foil or graphite on the surface of a supportinginsulatin disc, or may be of other well known resistance material. It ismerely necessary that the conducting portion be in the shape of arelatively thin, uniform, concentric, circular, annular disc.

The disc may be supported at the center by a low resistance metalbushing H which makes uniform electrical contact to the inner edge ofthe disc. It is supported on the outside by a low resistance metal ringl2 which makes electrical contact uniformly around the periphery of thedisc. The disc Il] may rest on insulation 29 which in turn rests againsta shoulder on the supporting elements II and I2. The ring 12 may bemounted on a base plate l3 of any convenient form and the bushing II isalso supported on the base plate l3 and insulating therefrom. Electricalconnection may be made to bushing II by means of a screw such as [4insulated from the base plate and electrical connection is made to thering l2 by means of screw 15. A battery I6 and adjustable seriesresistor H are placed in the circuit to supply electric current to thedisc Mounted above the disc ID is a movable slider or carrier 18 havinga spring pressed contact it which bears against the surface of the discH). The carrier [8. is guided on rod. 20' and screw 2i with which it ena es, the screw serving, thereby as a means for incving the slider alongthe radius of the. disc [0. Rod 20 and. screw 2| are supporteddiametrically across the disc In by means of end bearings 22 and 23,which are of insulating. material and conveniently supported on ring l2.The screw I 2| may be extended through bearing 23. and carry a crank oradjusting wheel and anv indicator dial 28' which indicates the radialposition of the contact l9. Screw 2| may be equipped with an inner stop2t which is set at a point so that the contactor [9 just begins tocontact disc in and an outer stop 25 set at some convenient outer limitof the scale. The latter is not necessarily the: outer boundary of thedisc, ie. the disc may extend beyond this point. A flexible lead 26connects to contactor l9 and serves to tap off the logarithmic voltagedesired, the potential being; measured between contactor l9 and centerpost Ii and read on a meter 21, which is preferably of a high resistanceor potentiometer type; v

The dial 28 and the screw 2| are together arranged so that this dialreads 1000 when the carriage I8 is against the'inner'sto 24 and thecontactor l9 just begins to contact the disc 10. There will at thispoint be 'zero potential indicated at 21. The screw 21 and the indicatordial may then be turnedto move the carriage i8 outward to someconvenient standard point, say the outer peripher of the disc, which maybe conveniently made ten times the radius of the inner bushing H. Apotential will at this point be indicated at 2'7 and this potential maybe adjusted by means of the resistor I! to indicate the value of thelogarithm to any. preassigned base, for the radius indicated on dial28'.

Thus, if it is desired to use the device to compute logarithms to thebase ten, resistor I7 is adjusted so that meter 21 reads. 1.000 voltswhen the dial 28 is set at radius 10.000. Then for all intermediatenumbers between 1.000 and 10.000 as set on dial 28, the meter 2'! willindicate the logarithm to the base ten.

If it is desired to determine the logarithm of numbers to the base etheresistor I1 is adjusted so, that meter 21 reads 2.302 volts when thedial 28 is set at radius 10.000. Intermediate settings of. dial 2% thenresult in the meter reading 21 being the natural logarithm of the dialsetting.

It is apparent that. any other. convenient base.

may be chosen for a particular problem or ap- 4 plication, it being onlynecessary to know the logarithm of one point on the dial scale to thebase desired. This evaluates the constant is in the equation e=k log T.

It is apparent that since the distribution of current in the disc isuniform and the current lines of flow are radial one may use instead ofa disc, a sector of an annulus as shown in Figures 3 and 4 as an. Such asector of an annulus may be cut with straight radial edges 4! and 42 andconcentric circular inner and outer boundaries 43 and 44, respectively,uniform electrical contact being made to circular inner edge 43 by meansof low resistance metal post 45 and uniform contact to the outercircular edge being by means of outer low resistance metal support 46,the latter conveniently being made integral with the base 41. Base 41supports at its opposite end the post 45 insulated therefrom by means ofwashers 58. Current flow is set up by passing a current from 45 to 46through battery as and rheostat 50. Carriage 5|, insulated from the baseand carrying contactor 52, is arranged in a manner similar to that shownin Figures 2 and 3, dial 53 being arranged to read 1.000 when thecontactor 52 is just beginning to make contact with the inner radius ofsector 30' and reads 10.000 at some convenient outer radius ten times aslarge. The latter is not necessarily the outer boundar of the annularsector and the sector may extend beyond this point. Logarithmic voltageis then obtained from a flexible lead 53 attached to the carrier El andconnected to the contactor 52. The potential difference is measured bymeter 5! connected between the lead 53 and the inner post t5. It can beshown mathematically that this variation of potential is alsologarithmic exactly as in the case of a disc. Adjustment of the currentthrough the potentiometer element 4E; is made in the same manner as thatdescribed in connection with Figures 2 and 3 and is accomplished byadjusting rheostat 50.

It is to be noted that it is not necessary to calibrate the resistor i0,Figure 2,.or 40, Figure If the disc or the disc sector is accuratelymachined and uniform in thickness and resistivity, this being relativelysimple of attainment,v then only one point of calibration, as aboveindicated, is required to adjust the base to whichlogarithmic variationapplies. This one setting calibrates the entire unit with a. high degreeof precision. This results because the logarithmic variation inpotential is not introduced by any empirical form of. the resistonbutrather results as an inherent property of the radial current flow in thethin conducting medium employed.

In order to preserve the precision of my invention, the terminalelements H and E2 of Figures 2 and 3 and 45 and 36 of Figures l and 5should be of much lower resistivity than the disc if] or sector 40. Theterminal elements are preferably made of copper or silver. Further,mechanical refinements in the slider-moving screw may be made in amanner well known in the art, and lost motion in the contactor is or 52is to be avoided. Also the indicator dial My invention may also be usedfor obtaining. antilogs in well known manner and in fact may;

be used for any computation involving the logarithm according to thewell known properties of the logarithm function.

The term "sector-like member, as used in the claims is defined as asector having any finite angle from 0 to 360 included between its radialboundaries. WHen the included angle is 360, such sector-like membertakes the fdrm of a disc.

What I claim as my invention is:

1. Apparatus for obtaining an electric signal which varies in alogarithmic manner with a linearly varying adjustment comprising auniform concentric circular annular disc of electrically conductingmaterial, means for flowing an electric current uniformly between theinner circular edge of said disc and the outer circular edge of saiddisc, means for electrically contacting a point on the surface of saiddisc, means for radially adjusting said contact point, and an outputcircuit connected between said contact point and an edge of said disc.

2. Apparatus for obtaining an electric signal which varies in alogarithmic manner with a linearly varying adjustment comprising auniform concentric circular annular sector-like member of electricallyconducting material, means for flowing an electric current uniformlybetween the inner circular edge of said sectorlike member and the outercircular edge of said sector-like member, means for electricallycontacting a point on the surface of said sector-like member, means forradially adjusting said contact point, and an output circuit connectedbetween said contact point and a circular edge of said sector-likemember.

3. Apparatus for computing logarithms comprising a uniform concentriccircular annular disc of electrical conducting material, means forintroducing an electric current at the inner edge of said disc, meansfor gathering the electric current uniformly around the outer peripheryof said disc, a radially adjustable contactor contacting the surface ofsaid disc, means for moving said contactor radially along said disc,means for positioning said contactor at a known radius, means foradjusting the electric current flowing through said disc, and means formeasuring the electric voltage between said contactor and an edge ofsaid disc.

4. Apparatus for computing logarithms comprising a uniform concentriccircular annular sector-like member of electrical conducting material,means for introducing an electric current at an inner circular edge ofsaid sector-like member, means for gathering the electric currentuniformly around the outer circular edge of said sector-like member,means for moving the contactor radially along the surface of saidsector-like member, means for positioning said contactor at a knownradius, means for adjusting the electric current flowing through saidsector-like member, and means for measuring the electric voltage betweensaid contactor and a circular edge of said sector-like member.

NORMAN D. COGGESHALL.

REFERENCES CITED The following references file of this patent:

UNITED STATES PATENTS are of record in the

